In this research, second order level set method for simulation of grain burn-back analysis is presented and compared with the first order level set according to discretisation technique, accuracy , and CPU time. In this manner and at the first step, we describe total necessities of level set method that are grid generation, minimum distance function calculation, relative condition estimation, ballistic characteristics calculation, and obtaining results. Then, at the second step, we  improve forth necessity of level set method by second order model. For validation of presented model, we consider many type of simple and complex grains and evaluate grain burn-back analysis. The obtained results indicate that second order model is more accurate than the first order model for simulation of complex grains. But, at the simple grains with more CPU time related to second order model, accuracy of two models are similar. A compromise between accuracy and CPU time suggest that one can use second order model for simulation of complex grains and first order model for simulation of simple grains.


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